If:
A) You don't have your Tefillin and the only pair available for you to borrow is for the opposite hand you generally use (ie, your dominant hand), or
B) You have a cast or splint on your arm or ...

In many societies, efforts are made to "convert" children who are naturally left-handed to using their right hands. As I understand it, modern neurology strongly frowns upon this practice.
I recall ...

There are many Halachos that a leftie does with his left hand and those that he does with his right hand. For example Shema is always done with the right hand even if you are a leftie. By which other ...